Physics-informed coupling strategies for machine-learning prediction of bubble detachment diameter from submerged orifices

Accurate prediction of bubble detachment diameter is essential for understanding and controlling interfacial area, residence time, and transport performance in multiphase systems. Existing mechanistic and empirical correlations often suffer from limited applicability under complex operating conditions, while purely data-driven machine learning (ML) models depend strongly on training-data coverage and may generalize poorly under small-sample or unseen-condition scenarios. This study investigates three physics-informed coupling strategies for extreme gradient boosting (XGBoost)-based prediction of the bubble detachment diameter, which are residual-on-physics-assisted XGBoost (RPA-XGBoost), input-augmented XGBoost (IA-XGBoost), and physics-constrained XGBoost (PC-XGBoost). These strategies incorporate a mechanism-guided semi-empirical correlation, rather than governing-equation or partial differential equation residual constraints as used in classical physics-informed neural network, at the output-residual level, input-feature level, and loss-function level, respectively. The results show that the coupling pathway strongly affects prediction accuracy, sample efficiency, and extrapolation robustness of ML models. On the test dataset, RPA-XGBoost achieves the best overall performance, with a mean absolute percentage error (MAPE) of 4.66%, because it preserved the dominant physical trend from the baseline correlation while learning only the nonlinear residual. Even training with only 68 samples, RPA-XGBoost maintains a MAPE of 9.30%, whereas purely data-driven XGBoost, IA-XGBoost, and PC-XGBoost exhibit pronounced overfitting and physically unreasonable trends. Validation on an independent extrapolation dataset further confirmed that residual-based physics-mechanism coupling strategy improves robustness under unseen operating conditions. These findings demonstrate that, for data-enhanced modeling of bubble dynamics, predictive accuracy and physical consistency depend not only on the learning algorithm itself but also on how physical information is coupled with the data-driven model.